Note: Often, you can change the formulation of a MILP to make it more easily solvable. For suggestions on how to change your formulation, see Williams [1]. |
After you run intlinprog once, you might
want to change some options and rerun it. The changes you might want
to see include:
Lower run time
Lower final objective function value (a better solution)
Smaller final gap
More or different feasible points
Here are general recommendations for option changes that are most likely to help the solution process. Try the suggestions in this order:
For a faster and more accurate solution, increase
the CutGenMaxIter option from its default 10 to
a higher number such as 25. This can speed up the
solution, but can also slow it.
For a faster and more accurate solution, change the CutGeneration option
to 'intermediate' or 'advanced'.
This can speed up the solution, but can use much more memory, and
can slow the solution.
For a faster and more accurate solution, change the IPPreprocess option
to 'advanced'. This can have a large effect on
the solution process, either beneficial or not.
For a faster and more accurate solution, change the RootLPAlgorithm option
to 'primal-simplex'. Usually this change is not
beneficial, but occasionally it can be.
To try to find more or better feasible points, increase
the HeuristicsMaxNodes option from its default 50 to
a higher number such as 100.
To try to find more or better feasible points, change
the Heuristics option to either 'round' or 'rins'.
To attempt to stop the solver more quickly, change
the TolGapRel option to a higher value than the
default 1e-4. Similarly, to attempt to obtain a
more accurate answer, change the TolGapRel option
to a lower value. These changes do not always improve results.
For a more accurate solution, decrease the RelObjThreshold option
from its default 1e-4 to a smaller positive value
such as 1e-6. This change can cause intlinprog to
take more time to solve the problem, and to find more integer feasible
points during its solution process.
Often, some supposedly integer-valued components of the solution x(intcon) are
not precisely integers. intlinprog considers
as integers all solution values within the TolInteger tolerance
of an integer.
To round all supposed integers to be precisely integers, use
the round function.
x(intcon) = round(x(intcon));
Caution Rounding can cause solutions to become infeasible. Check feasibility after rounding: max(A*x - b) % see if entries are not too positive, so have small infeasibility max(abs(Aeq*x - beq)) % see if entries are near enough to zero max(x - ub) % positive entries are violated bounds max(lb - x) % positive entries are violated bounds |
intlinprog does not enforce that solution
components be integer valued when their absolute values exceed 2.1e9.
When your solution has such components, intlinprog warns
you. If you receive this warning, check the solution to see whether
supposedly integer-valued components of the solution are close to
integers.
intlinprog does not allow components of
the problem, such as coefficients in f, A,
or ub, to exceed 1e15 in absolute
value. If you try to run intlinprog with such
a problem, intlinprog issues an error.
If you get this error, sometimes you can scale the problem to have smaller coefficients:
For coefficients in f that are
too large, try multiplying f by a small positive
scaling factor.
For constraint coefficients that are too large, try multiplying all bounds and constraint matrices by the same small positive scaling factor.
[1] Williams, H. Paul. Model Building in Mathematical Programming. Wiley, 2013.